Yong, Jiongmin Optimal controls for distributed parameter systems with mixed constraints. (English) Zbl 0731.49031 Colloq. Math. 60/61, No. 1, 35-48 (1990). The author establishes a Pontryagin type maximum principle for an optimal control problem with mixed constraints, governed by the semilinear evolution equation \(x'(t)=Ax(t)+f(t,x(t),u(t)),\quad t\in [0,T],\) where A is the infinitesimal generator of a \(C_ 0\)-semigroup on a Banach space and f is strongly measurable in t, Lipschitz continuous in x and continuous in u. The main tool in the present approach is the Ekeland’s variational principle. The notion of Clarke’s generalized gradient is used. Reviewer: C.Popa (Iaşi) MSC: 49K27 Optimality conditions for problems in abstract spaces Keywords:Pontryagin type maximum principle; mixed constraints; semilinear evolution equation; Ekeland’s variational principle; Clarke’s generalized gradient PDFBibTeX XMLCite \textit{J. Yong}, Colloq. Math. 60/61, No. 1, 35--48 (1990; Zbl 0731.49031) Full Text: DOI